Michael and Melanie Bellanger Boyer, transplanted Parisians who live in a snug one-bedroom in the West 90s, are members of what social scientists sometimes call the “forgotten middle.”

Mr. Boyer, 29, earns $86,000 a year as a financial auditor. His wife, 31, earns $19,000 working at an animal shelter, where a modest salary is offset by generous benefits, a boon since the birth of a daughter, Nora, in January.

Last August, the couple moved to a 500-square-foot space for which the rent is $2,700. With such attractions as exposed brick, an ornately carved fireplace and a location just steps from Central Park, the apartment was the nicest and most affordable one they could find. But the hefty rent check they write every month takes an increasing toll.

“If it weren’t for the high rent, I could afford to stay home with the baby,” Ms. Bellanger Boyer said, noting that the family’s monthly expenses now include $2,000 for child care. “But I needed to keep my job because we need my benefits, and so we had to put Nora in day care.”

Households like this — middle-income in terms of earnings but paying at least 30 percent of those earnings for housing — perch on the knife edge between hope and anxiety. Even as their housing costs mount, they struggle to hang onto their apartments because they know that their options can only narrow, given the city’s challenging housing market. Those lucky enough to be ensconced in rent-regulated units, a dwindling commodity, hang onto them for dear life.

And in Manhattan, where such households are most prevalent, the situation is especially acute. These residents fear, often correctly, that if they lose their current berth, they will be forced not just out of the borough but out of the city, a move that may result in a longer commute and less family time.

This population includes young middle-class families like the Boyers, burdened with child care expenses, along with elderly New Yorkers living on fixed incomes, and young singles earning starter salaries and doubling, tripling or quadrupling up in pocket-size quarters to acquire a New York lifestyle. And their situation is attracting growing attention.

On May 5, Mayor Bill de Blasio announced a $41 billion plan to provide additional affordable housing for middle-income as well as low-income New Yorkers.

A few weeks earlier, the Furman Center for Real Estate and Urban Policy of New York University and Capital One Bank jointly issued a report titled “The Affordable Rental Housing Landscape,” showing that low-income New Yorkers are not the only city residents to be rent-burdened — that is, to pay at least 30 percent of their gross income for rent and utilities. Among middle-income households — for example, a three-person household earning between $91,000 and $152,000 annually — 14 percent or roughly 290,000 households fell into this category in 2012.

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Diane Ordelheide’s studio was a squeeze in every way; she has decamped for Florida.CreditRobert Caplin for The New York Times

“We examined the situation because rental housing has become less affordable in the past six years,” said Max Weselcouch, the director of the Moelis Institute for Affordable Housing Policy at the Furman Center. “Between 2005 and 2008 things looked pretty good. The median income rose, and new housing construction was at a peak. But between 2009 and 2012, there was little new construction even as preliminary estimates show that up to 200,000 new residents arrived in New York.”

The experiences of families like the Boyers put flesh on the numbers. The couple were taken aback by hefty upfront costs that included a broker’s fee and a two-month deposit (one of the months because of their dog). And space is at a premium. A crib and baby carriage nestle next to the double bed in the bedroom, a playpen dominates the living room, and a car seat atop a dining chair doubles as a highchair. But most stressful is the anxiety about the future.

“I can’t complain,” Mr. Boyer said. “We have a decent life. But we worry that we can’t save any money. If we have major health care expenses, we wouldn’t have saved enough to cover them. If we were in France, we might be paying the same percent of our salary for rent, but items like health care would be covered.

“Our back is against the wall,” he added. “Manhattan is nice when you’re young, but with a baby it’s really hard. We need more space, and we’re paying 31 percent of our income for rent.”

Although the couple yearns to stay in the borough, they suspect that when their lease expires in August they will have to move farther afield, hopefully to a place carrying a more modest price tag.

There are compelling reasons middle-income families might choose to pay a higher than desirable rent for the benefit of living in a metropolis like New York, which offers so much in the way of jobs, safety, a lively lifestyle and cheap transportation.

“It may be a rational choice to pay more to live here because you get so much,” said Matthew Gordon Lasner, an assistant professor in the Urban Affairs and Planning Department of Hunter College. But in his opinion, middle-income families often pay an unexpectedly steep emotional price for the privilege.

“In New York, it’s not just the poor in Jacob Riis-type conditions who endure housing stress,” said Professor Lasner, the author of the book “High Life: Condo Living in the Suburban Century” (Yale University Press, 2012). “When it comes to housing, middle-income families also need help. They earn too much to qualify for apartments earmarked for low-income families, but they can’t afford market-rate housing. So they feel very vulnerable. They get that letter telling them their rent is going up, and they realize they’re one pen stroke away from being displaced, from having to pay a lot more for a new apartment, or worse, having to leave the city.

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From left, Dana Bakich, Cecillia Costa and Danielle Dormand share a two-bedroom on the East Side.CreditKatherine Marks for The New York Times

“They’re truly the forgotten middle, locked out of both luxury and public housing,” said Professor Lasner, whose department recently published a report titled “Where Will New Yorkers Live?” that underscored the shrinking number of affordable rentals for middle-income households. “They don’t experience as much stress as low-income families, but they live with a tremendous amount of uncertainty.”

New York is a city of renters — according to the Furman Center, two-thirds of the city’s three million households rent — and this is one reason the center and Capital One focused on this population in their report. Of the city’s rental units, 45 percent are stabilized or controlled, 8 percent are in public housing, 8 percent are subsidized, and the rest are market rate.

For generations, middle-income New Yorkers found it relatively easy to land an affordable place to live. But soaring rents sparked by a tight-as-a-drum real estate market, combined with a dwindling number of rent-regulated apartments, stagnant wages, and a burgeoning population fueled by the city’s growing allure, have transformed this landscape.

In Manhattan, which Ms. Weselcouch of the Furman Center described as “the epicenter of fear,” the situation is especially acute. Rents in the borough have climbed more than any others in the city, up by 19 percent between 2005 and 2012. During those years, the rents of one quarter of the previously regulated units in the borough were deregulated.

Three 20-somethings from Florida who moved in January to a 900-square-foot apartment on East 39th Street can speak firsthand about how difficult it can be to establish a toehold in this landscape.

The three are Cecillia Costa, Dana Bakich and Danielle Dormand. All have full-time jobs in sales, and Ms. Dormand moonlights as a cocktail waitress several evenings a week. Their combined annual salaries come to just under $150,000.

In January, their broker, Dan Falconetti of Citi Habitats, found them a two-bedroom with a view of the East River and a balcony Ms. Costa liked so much that she put a picture of it on her Facebook page. A temporary wall allowed them to carve a third bedroom out of the living room. Their total monthly rent is $4,100.

Like so many newcomers, the three were drawn by the city’s sense of promise and possibility, a chance to reinvent themselves and reinvigorate their lives.

“I wanted something new and different,” Ms. Bakich said. “I wanted to go bigger. I didn’t have a job, but I’d saved, and I figured I’d just make it work — no ifs, ands or buts.”

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The roommates put up a temporary wall in the living room to create a third bedroom.CreditKatherine Marks for The New York Times

Ms. Costa put it another way: “I moved here to change my life.”

To save on groceries, they take advantage of perks like free yogurt and cereal available in their offices.

“And movies are so expensive,” Ms. Bakich said, “I’ve been only a few times since I arrived in the city a year and a half ago, even though I used to go all the time.”

For women used to balmy weather year-round, big-ticket wardrobe items like boots and winter coats are prohibitive. “I haven’t bought a single article of clothing since January,” Ms. Costa said. “I haven’t even gone into a store. You can’t.”

Furnishing the apartment also proved daunting. “We bought one thing per paycheck,” Ms. Costa said. “I had no lamp in my bedroom for two weeks.” Two weeks ago they bought a toaster.

“And nails, eyebrows — they’ve gone out the window,” Ms. Dormand said. “I use box hair dye. I eat dollar pizza, and I’ve learned to like it. Broke in Florida isn’t like broke here. Here, $40 gets you nowhere, not even out of the house.”

Finances are such a constant worry that until recently, when she stopped working on commission, she dreaded opening her paycheck on Fridays.

Yet all three are, at least for now, willing to make the sacrifices necessary to buy themselves a Manhattan lifestyle.

“I feel very proud of myself, and everyone is proud of me,” Ms. Dormand said. “I didn’t just move away, I moved to Manhattan.” She is even proud to write her address: New York, New York.

Their broker understands the trade-offs. Mr. Falconetti recently agreed to pay $1,500 a month to live with six other people — “at least I hope there are only six,” he said — in a seven-bedroom loft in Williamsburg. “If you’d have asked me when I first came to New York in 2008 whether I’d have done something like this,” he said, “I’d have said, ‘No way.’ Now I’m jumping at the opportunity.”

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Ms. Bakich and Ms. Costa have become accustomed to pinching pennies.CreditKatherine Marks for The New York Times

Along with the mayor’s new housing plan, other efforts are underway. New York City Councilwoman Helen Rosenthal, whose district covers much of the Upper West Side, is seeking ways to make more units in luxury buildings available to middle-income families.

“A family of four earning from $84,000 to $140,000 is the hole in the doughnut,” Ms. Rosenthal said, “and we don’t have a way to address that group.”

She can already point to one modest victory. Her office worked with TF Cornerstone, which is building a 1,025-unit luxury tower at 606 West 57th Street, to increase to 220 from 205 the number of units set aside for families of four earning about $150,000 annually.

But the demand for such housing far outstrips the supply, as Laura Bailey, the managing vice president of community development finance at Capital One, which helps finance projects that include units for middle-income families, can testify.

“At Macedonia Plaza in Flushing, Queens, we got 40,000 applications for 100-plus units,” Ms. Bailey said. “At Sugar Hill Apartments in Harlem, we had 48,000 applications for 98 units. There’s a certain amount of heartache you can see through the numbers.”

For rent-stressed middle-income New Yorkers, the greatest fear may be that they are one rent increase, or one layoff, away from having to depart New York for good.

This is what happened to Diane Ordelheide, 63, who moved from St. Louis to New York in 2002 to pursue a lifelong dream, a career as an actress. In that goalshe succeeded, landing roles in “Law and Order,” “All My Children” and several movies and commercials.

But despite a $30,000-a-year pension from her quarter century as a teacher, finding affordable housing proved increasingly elusive. Ms. Ordelheide hopscotched from neighborhood to neighborhood, finally alighting three years ago in a renovated studio on West 102nd Street for which the monthly rent was $1,635. Though she estimates that the space was just about 200 square feet, she was charmed by the Murphy bed and the modern kitchen, accented with granite and stainless steel.

At a certain point, however, Ms. Ordelheide realized that she could no longer afford to remain in the city.

“I wanted to stay here so bad,” she said. “The city changed my life, and I couldn’t imagine leaving. But one day I just realized that I couldn’t do this anymore. It was too scary. I came to the conclusion that I had to get out of the city. And once I decided, except for the sense of sadness, I felt a great relief.”

On May 11, Ms. Ordelheide packed up her guitar, banjo and other possessions, and set off for a cottage in Pompano Beach, Fla. — monthly rent, $1,345.

“I’m trying to be positive because I have no choice,” she said as she was getting ready to leave. “I’m hoping that because I’m taking a lot of my things with me, the move will be easier. Still, it’s really hard.”

Correction:

An article on June 1 about the high percentage of their incomes that middle-class New Yorkers often pay for housing in Manhattan misstated the incomes of Michael and Melanie Belanger Boyer. Mr. Boyer makes $86,000 a year, not $90,000; Ms. Belanger Boyer makes $19,000, not $21,000.